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# Accession Number:

## AD0672207

# Title:

## RANDOM ORDINARY DIFFERENTIAL EQUATIONS.

# Descriptive Note:

## Technical rept. Sep 67-Jun 68,

# Corporate Author:

## CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

# Report Date:

## 1968-06-01

# Pagination or Media Count:

##
52.0

# Abstract:

## Existence and uniqueness theorems are proved for solutions in the mean of the random differential equation x ft,x,omega. This is accomplished by determining when a sample path solution is also a solution in the mean. The usual definition of mean stability is generalized to a more useful form. Theorems are developed which relate this general type stability to the stability of the average problem. Finally theorems relating almost sure stability with the stability of the average problem are proved. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#